Southampton captain, Fonte raised high to head in a corner kick played by Ward Prowse, with the ball coming off the back of Lukaku and into the back of the net.
Everton tried to get back into the game, but could not find their way back as Southampton held onto the lead going into the interval.
The second half saw the Saints start the better of the two teams and enjoying a good spell of possession.
It did not take long in the second half for Southampton to increase their lead to 2-0 with Clyne setting-up Pelle for the second goal of the match.
The Italian beat Tim Howard with an easy tap-in to give his team a comfortable lead.
Southampton wrapped up the game with the third goal in the 83rd minute, as Yoshida rose above Everton's defenders, to get his name on the score sheet.
Lukaku had a chance late in the match to get one back, but drove his effort into Foster's hands, as Southampton took away the three points.
